Statistics and Probability Answers

The loss due to an earthquake in a commercial building is modelled by a random
variable X with density function
f(x) = 
0.005(20 − x), for 0 < x < 20
0, elsewhere
Given that the fire loss exceeds 10, what is the probability that it exceeds 18

Suppose an airline accepted 12 reservations for a commuter plane with 10 seats. They know that 7 reservations went to regular commuters who will show up for sure. The other 5 passengers will show up with a 50% chance, independently of each other.

(a) Find the probability that the flight will be overbooked.

(b) Find the probability that there will be empty seats.

Suppose that 3% of computer chips produced by a certain machine are defective. The chips are put into packages of 20 chips for distribution to retailers. What is the probability that a randomly selected package of chips will contain at least 2 defective chips

Tests on the breaking strengths if 10 cables were made and showed a mean strength of 1200 psf and a standard deviation of 100 psf. Estimate the (a) mean and the (b) standard deviation of the population of all the cables being produced by the company.

1. The recorded measurements of sample of soil cohesion are 96, 106, 97, 88, 102 and 94 KPa respectively. (a) Compute the sample mean cohesion. This is considered as the unbiased and efficient estimate of the population mean. (b) Compute the sample variance. (c) Compute the estimated population variance by multiplying the sample variance by (n/n-1). (d) Compare the sample standard deviation with the estimated population standard deviation.

Suppose that an airline company claims that the average weight of checked baggage is less than 15 pounds. To support the claim, the airline company conducts a random sample of 150 passengers and finds that the average weight of checked baggage is 14.2 pounds, with a standard deviation of 6.5 pounds. Do these data support the airline company's claim at the α = 0.05 level of significance? Use s = 6.5 as an estimate for since n 30.

A semiconductor manufacturer produces controllers used in automobile engine applications. The customer required that the process fallout or fraction defective at a critical manufacturing step not exceed 0.05 and that the manufacturer demonstrate process capacity at this level of quality using α = 0.05. The semiconductor manufacturer takes a random sample of 200 devices and finds that four of them are defective. Can tha manufaturer demonstrate process capability for the customer?

Suppose that a campaign manager claims that the percent of registered voters who prefer his candidate is 60 percent. A pollster conducts a random survey of 500 registered voters to test the campaign manager's claim and finds that 58 percent of the sample of registered voters preferred the campaign manager's candidate. Perform the test of hypothesis at the α = 0.10 level of significance.

Q3. (Write down the measurement unit when applicable and correct your answers to 4 decimal places.)
A factory claims that the net weight of a bag of chips follows a Normal distribution with population standard deviation 1.5 grams, without disclosing the population mean weight. John is interested in knowing the population mean. He wants to estimate the population mean weight by himself. He buys 22 bags of chips and found that the total weight of 22 bags of chips is 1650 grams.
(a) Find a point estimate of the population mean weight of a bag of chips based on John’s information. (2 marks)
(b) Calculate the sampling error at 95% confidence. (5 marks)
(c) Construct a 95% confidence interval of the population mean weight of a bag of chips.

The rejection or acceptance of a hypothesis is dependent on the statistical interval of the critical values which is dictated by the confidence level or level of significance. A 95% level of confidence means a 0.05 level of significance. Sometimes a hypothesis is rejected at 0.01 but accepted at 0.05. When this happens, which level of significance would you adopt and why.